Research Journal of Applied Sciences, Engineering and Technology 6(14): 2601-2606, 2013
ISSN: 2040-7459; e-ISSN: 2040-7467
© Maxwell Scientific Organization, 2013
Submitted: March 05, 2013
Accepted: April 02, 2013
Published: August 10, 2013
Research on High Frequency Model of Hybrid Vehicle Battery
Yang Yongming, Yao Mo and Wang Quandi
School of Electrical Engineering, Chongqing University, Chongqing, 400044, China
Abstract: The application of motor and converter in hybrid vehicle can lead to a significant increase in
electromagnetic compatibility. The influence of traction batteries as part of the electromagnetic interference path
was not well considered. In this study, high frequency circuit models of single cell, cells connected in series and
cells connected in parallel were proposed and developed based on their impedance characteristics and their structure
features. Finally, values calculated based on the models and dates measured actually were compared and analyzed.
The results show the calculation high frequency losses and the simulation as interference path.
Keywords: Batteries, EMC, hybrid vehicles, impedance, modeling
INTRODUCTION
With resources and environment problems being
increasingly serious, hybrid cars are rapidly developed
by Madi et al. (2008). However, the battery pack, as
one of the hybrid cars power source, is directly
connected to the DC/AC inverter to provide energy to
the drive motor, which makes high frequency harmonic
interference signals produced by the power switching
device transmitted though the battery pack and then
produce electromagnetic compatibility problems by
Ehsani et al. (2007) and Mutoh et al. (2005), similar
work by Omar et al. (2012). So study the frequency
characteristic of the power battery, set the high
frequency model of battery is of great significance to
electromagnetic interference suppression and system
modeling and simulation of electromagnetic
interference.
MATERIALS AND METHODS
For the power batteries, when the frequency is
higher than 1kHz, polarization effect of the battery on
its impedance characteristics is very small, while the
skin effect of the battery electrode and the connecting
wire make a big difference. The impedance of battery
electrolyte plays a decisive role in the battery
impedance characteristics by Chen et al. (2006) and
Aesic and Wei (2011), similar work by Zhang et al.
(2010). The electrode impedance mainly functions as
the resistance and inductance of the electrode and the
capacitance polarization effect is so small that the
impedance of the electrolyte can be treated as a
resistance.
For batteries' high-frequency modeling, the
actually porous electrode was taken as cylindrical
electrode and due to the skin effect the calculation
Fig. 1: A conductor internal electromagnetic induction
method of high-frequency resistance differs from DC
resistance.
At low frequencies, the current density distribution
inside the conductor is uniform. From the conductor
cross-section, current flow is the same in the center and
the edge area. While at high frequencies, current
density of conductor surface becomes large and there is
almost no current flow in the center regional. It is called
the skin effect that the low frequency current evenly fill
the entire wire while high frequency current only flows
through the surface region of the conductor.
When a high frequency current flow into a
cylindrical conductor, longitudinal section of
cylindrical conductor as shown in Fig. 1, it will
generate a changing magnetic field inside the
conductor. If a current direction is horizontal to the left,
it will generate a magnetic field as is shown in the
internal conductor, Induction electromotive force will
be produced in the planar abcd and efgh. This Induction
EMF will cause eddy currents in the conductor to
prevent the change of flux. Inside the conductor the
direction of eddy cb and he is opposite to the main
current, which weakens the current, while, in the
surface of the conductor the direction of vortex ad and
fg is the same with the main current, the current was
Corresponding Author: Yang Yongming, School of Electrical Engineering, Chongqing University, Chongqing, 400044,
China
2601
Res. J. Appl. Sci. Eng. Technol., 6(14): 2601-2606, 2013
Fig. 2: Skin impedance diagram
strengthen. As a result current tends to flow through
from the surface of the conductor.
For the high-frequency circuit, the change rate of
current is very huge, the phenomenon of uneven
distribution will be more serious. The maximum EMF
was induced in the center area of the conductor by the
magnetic field generated by the high-frequency current
in the conductor. Since the induction electromotive
force generates an induction current in the closed
circuit, the maximum induced current appears in the
center of the conductor, which is contrary to the
direction of the primary current, as a result it force the
current close to the outer surface of the conductor.
Thus, the internal conductor is actually no current and
current is concentrated in a thin layer adjacent to the
wire outer. Results in the increase of its impedance
value. Therefore, calculating the high-frequency
impedance of the conductor skin effect must be
considered, as is shown in Fig. 2 cylindrical electrode
resistance is calculated:
From the basic formula of conductor resistance:
R
Fig. 4: External inductance calculation diagram
''
inductance L , which is generated by flux that linked
the entire conductor current:
(1)
l
Fig. 3: Internal inductance calculation diagram
 S
L  L'  L''
where,
l
= The length of the conductor
S = The cross-sectional area of the conductor
y = The conductivity of the conductor
(3)
As Fig. 3 shows, the internal inductance:
When   R :
When high frequency current is applied, the current
is concentrated in a thin layer of the outer conductor
surface, the effective cross-sectional area S  2r  d
2 , ( µis the
.where d is the penetration depth d 
B
0 I '

 I
I
 2  0 2
 0
2 2 R 2
2R
(4)
internal flux of the electrode:
2 f 
permeability of the electrode).Thus under the effect of
high frequency current the resistance of cylindrical
conductor electrode is as follows:

Rac ( f ) 
 f l
4r 2 
d ' 
'
(2)
 Ih
I'
2
d  2 d  0 4  3 d
I
2R
R
 0 Ih
2R 4

R
0
 3 d 
 0 Ih
8
(5)
(6)
The internal inductance of one electrode:
Inductance generated by the current carrying
electrodes which are composed of two parts: one part is
'
the internal inductance L ,which is generated by the
magnetic flux inside the conductor that linked only
parts of the conductor, the other part is the external
L' 
'
I

0h
8
The external inductance is shown in Fig. 4.
2602 (7)
Res. J. Appl. Sci. Eng. Technol., 6(14): 2601-2606, 2013
The magnetic vector potential generated by those
two electrodes: A   0 I ln r1 , where r1, r2 denotes the
2
r2
distance between the field point and the positive
current, the negative current.
External magnetic flux of the two electrodes:
 ''     A  dl
l
0 I 
DR
DR 
dl   ln
dl 
 ln
cd
R
R
2  ab

 0 Ih D  R

ln

R
Fig. 5: High frequency equivalent model of the battery
(8)

The external inductance of the two electrodes:
 h DR
L 
 0 ln
I

R
''
 ''
(9)
Fig. 6: Masurement methods
The electrode inductance:
L  L'  L'' 
0h

DR
 2  0 ln

R
8
(10)
 h 
DR
 0  0 ln

R
4
where,
D = The distance between the two electrodes
R = The electrode equivalent radius
When frequencies higher than 1kHz, the
polarization effect of the battery is not obvious, the
equivalent impedance of the electrolyte within the
battery can be equivalent to R0 . Therefore, the high
(a) Amplitude-frequency
frequency equivalent model of the battery can be
modeled as shown in Fig. 5.
The complex impedance is measured with the
Agilent impedance analyzer 4294A and its standards
measurements fixture 16047E, shown in Fig. 6.
To get the measurement impedance value of the
battery, the impedance of block condenser must be
removed from the total measurement result. The
computation process of battery impedance is derived as
follows:
Z total  Z bat  Z cap  Re( Z total )  j Im( Z total )
(11)
Z cap  Re （ Z cap）  j Im( Z cap )
(12)
(b) Phase-frequency
Z bat  Z total  Z cap
 Re （Z total） Re （Z cap） j[Im( Z total )  Im（Z cap）
]
 Re( Z bat )  j[Im( Z bat )]
Fig. 7: The impedance calculation results of the single cell
The value of measurement and model for cell is
(13)
shown in Fig. 7, compare the measured impedance
2603 Res. J. Appl. Sci. Eng. Technol., 6(14): 2601-2606, 2013
(a) Amplitude-frequency
(a) Amplitude-frequency
(b) Phase-frequency
Fig. 8: Comparison of measured and simulated impedance
curves for a cell
curve and the calculated impedance curve and then
analyze the causes of the error. Because the power
battery is not used alone in the practical application and
generally used on multiple cells in series to raise the
output voltage, multiple cells in parallel to increase the
output power, the high frequency characteristics of cells
connected in series and in parallel were also analyzed in
this study.
The comparison of the measured impedance curve
and the calculated impedance curve is shown in Fig. 8.
Take four cells connected in series for example.
The impedance of four cells in series is about four times
the value of single battery cell, however, the connection
between the battery cells will produce a parasitic
capacitance effection and the connecting wires between
the batteries will affect their impedance values, taking
those into account the calculation results also need to be
corrected.
The model parameters of battery in series:
Rseries  4 （R0  Rac ( f )） k1 ， Lseries  4  L - k2
(b) Phase-frequency
Fig. 9: Comparison of measured and simulated impedance
curves for cells in series
where k1  0.046 is the correction factor for the resistance value of batteries in series, k2  1.865 108 is the
correction factor for the inductance value. Figure 9
shows the comparison of the measured impedance
value and the calculated impedance value.
The agreement between measured and simulated
value of the impedance shows the suitability of the
proposed conducted EMI model for the series battery,
which illustrates that the high frequency model of series
battery can be correctly derived through the model of
the battery cell.
The connection of cells in parallel is shown in
Fig. 10, Battery connection wires is a special kind of
steel that can effectively inhibit skin effect, therefore,
the conductor resistance can be so small that to be
ignored; because of parallel connection manner, the
inductance between the connecting wire is still
relatively large, and the external inductance L ' '
of the conductor is far larger than the internal
inductance L' ,for what the inductance of the connecting
2604 Res. J. Appl. Sci. Eng. Technol., 6(14): 2601-2606, 2013
The model parameters of battery in parallel:
1
R parallel   R0  Rac  f   k3
4
where k3  0.03 is correction factor for the inductance
value of batteries in parallel. Figure 12 shows the
comparison of the measured impedance curve and the
calculated impedance curve.
Since the steel connected between the cells will
affect the overall impedance of the battery pack, and
also the series-parallel connection of the batteries may
causes the parasitic capacitance between the electrodes
and the parasitic inductance on the connecting steel,
there is a certain error between the model calculated
values and the actual measured values.
Fig. 10: Four cells connected in parallel
Fig. 11: Eequivalent inductance for cells in parallel
CONCLUSION
A method to establish the high frequency circuit
model of the battery based on its impedance
characteristics and the structure of battery cell is present
in this study. The high-frequency circuit model of
battery are developed including instructions for
calculating the model's parameter. The high-frequency
models of cell, cells connected in series, cells connected
in parallel are validated by the measurement in the
frequency range from 150 kHz to 30 MHz. the
measured impedance value of the battery and the
calculated impedance value were compared to analyze
the causes of the error. The results allow the prediction
of the conducted behavior of the battery including the
high frequency losses where batteries mainly react as an
inductance with a comparatively high impedance, also
it allows to predict the effect of batteries as spreading
path for EMI and the external electric fields and
magnetic fields generated by the batteries.
(a) amplitude-frequency
ACKNOWLEDGMENT
The study is financially supported by National
Natural Science Foundation of China Project51177183.
(b) phase-frequency
REFERENCES
Fig. 12: Comparison of measured and simulated impedance
curves for cells in parallel
wire cannot be ignored. the length of connecting steel
between each of the two battery cells is with half of the
electrode, combining with the method of calculation of
the conductor inductance, inductance value of the
connecting wire is 1/2 of the pair of electrodes, the
equivalent inductance series-parallel circuit diagram in
Fig. 11:
L parallel 
171
LL
170
(14)
Aesic, K. and Q.A. Wei, 2011. Hybrid battery model
capable of capturing dynamic circuit characteristics
and nonlinear capacity effects. IEEE T. Energy
Conver., 26(12): 1172-1180.
Chen, M., A. Gabriel and M. Rincon, 2006. accurate
electrical battery model capable of predicting
runtime and I-V performance. IEEE T. Energy
Conver., 21(7): 504-511.
Ehsani, M., G. Yimin and J.M. Miller, 2007. Hybrid
electric vehicles: architecture and motor drives.
Proc. IEEE, 95(4): 719-728.
2605 Res. J. Appl. Sci. Eng. Technol., 6(14): 2601-2606, 2013
Madi, A., J.L. Young and K. Rajashekara, 2008. Power
electronics and motor drives in electric, hybrid
electric and plug-in hybrid electric vehicler. IEEE
T. Ind. Electron., 55(6): 2237-2245.
Mutoh, N., M. Nakanishi, M. Kanesaki and J.
Nakashima, 2005. EMI noise control methods
suitable for electrical vehicles drive systems. IEEE
T. Electromagn. C., 47(12): 930-937.
Omar, H., V.M. Joeri and L.A. Philippel, 2012.
Modeling and implementation of a multidevice
interleaved DC/DC converter for fuel cell hybrid
electric vehicle. IEEE T. Power Electr., 27(11):
4445-4458.
Zhang, J., S.C. Sharif and M. Alahmad, 2010. Modeling
discharge behavior of multicell battery. IEEE T.
Energy Conver., 25(12): 1133-1141.
2606